For Aliyah’s graduation party, her mom made her a chocolate cake. Her siblings ate 1/4

Question

of the cake, and her friends ate 2/3
of the cake. How much of the cake was left?

Desmos Scientific Calculator

(1 point)
Responses

3/4
3 fourths

1/2
1 half

1 12
1 over 12

5/6

plz give me a correct answer

Answer 1

To find out how much of the cake is left, we first need to determine how much cake was consumed by Aliyah's siblings and friends.

1. Aliyah's siblings ate \( \frac{1}{4} \) of the cake.
2. Her friends ate \( \frac{2}{3} \) of the cake.

To find the total amount of cake eaten, we need to add these fractions:

\[ \text{Total eaten} = \frac{1}{4} + \frac{2}{3} \]

To add these fractions, we need to find a common denominator. The least common denominator (LCD) of 4 and 3 is 12.

Now, we can convert each fraction:

\[ \frac{1}{4} = \frac{3}{12} \quad (\text{multiply the numerator and denominator by 3}) \] \[ \frac{2}{3} = \frac{8}{12} \quad (\text{multiply the numerator and denominator by 4}) \]

Now we can add the converted fractions:

\[ \frac{3}{12} + \frac{8}{12} = \frac{11}{12} \]

So, \( \frac{11}{12} \) of the cake has been eaten.

To find out how much of the cake is left, we subtract the amount eaten from the whole cake (which is \( 1 = \frac{12}{12} \)):

\[ \text{Cake left} = 1 - \frac{11}{12} = \frac{12}{12} - \frac{11}{12} = \frac{1}{12} \]

Therefore, the amount of cake left is \( \frac{1}{12} \).

Answer 2

are you sure

Answer 3

Yes, the calculations can be summarized as follows:

1. Calculate the amount consumed by Aliyah's siblings and friends:

   • Siblings ate: \( \frac{1}{4} \)
   • Friends ate: \( \frac{2}{3} \)

2. Add the two fractions:

   • Find a common denominator (the least common denominator for 4 and 3 is 12):
     • Convert \( \frac{1}{4} \) to \( \frac{3}{12} \)
     • Convert \( \frac{2}{3} \) to \( \frac{8}{12} \)

   So now we have: \[ \frac{1}{4} + \frac{2}{3} = \frac{3}{12} + \frac{8}{12} = \frac{11}{12} \]

3. Calculate the amount of cake left:

   • Start with the whole cake, which can be represented as \( 1 \) or \( \frac{12}{12} \).
   • Subtract the amount eaten: \[ \text{Cake left} = 1 - \frac{11}{12} = \frac{12}{12} - \frac{11}{12} = \frac{1}{12} \]

So, the correct answer is indeed \( \frac{1}{12} \) of the cake is left.